Redesigning metabolic networks using mathematical programming

The design of new generation bioprocessing plants is increasingly dependent on the design of process-compatible microorganisms. The latter, whether through genetic or physiological manipulations, can be greatly assisted by metabolic engineering. An emerging powerful tool in metabolic engineering research is computer-assisted cell design using mathematical programming. In this work, the problem of optimizing cellular metabolic networks has been formulated as a Mixed Integer Nonlinear Programming (MINLP) model. The model can assist genetic engineers to identify which cellular enzymes should be modified, and the new levels of activity required to produce an optimal network. Results are presented from the tricarboxylic acid cycle in Dictyostelium discoideum. Copyright 1998 John Wiley & Sons, Inc.     

Assembling networks of microbial genomes using linear programming

Background  

Microbial genomes exhibit complex sets of genetic affinities due to lateral genetic transfer. Assessing the relative contributions of parent-to-offspring inheritance and gene sharing is a vital step in understanding the evolutionary origins and modern-day function of an organism, but recovering and showing these relationships is a challenging problem.     

Discovery of Boolean metabolic networks: integer linear programming based approach

Background

Traditional drug discovery methods focused on the efficacy of drugs rather than their toxicity. However, toxicity and/or lack of efficacy are produced when unintended targets are affected in metabolic networks. Thus, identification of biological targets which can be manipulated to produce the desired effect with minimum side-effects has become an important and challenging topic. Efficient computational methods are required to identify the drug targets while incurring minimal side-effects.

Results

In this paper, we propose a graph-based computational damage model that summarizes the impact of enzymes on compounds in metabolic networks. An efficient method based on Integer Linear Programming formalism is then developed to identify the optimal enzyme-combination so as to minimize the side-effects. The identified target enzymes for known successful drugs are then verified by comparing the results with those in the existing literature.

Conclusions

Side-effects reduction plays a crucial role in the study of drug development. A graph-based computational damage model is proposed and the theoretical analysis states the captured problem is NP-completeness. The proposed approaches can therefore contribute to the discovery of drug targets. Our developed software is available at “http://hkumath.hku.hk/~wkc/APBC2018-metabolic-network.zip”.

     

Analysis of the pathway structure of metabolic networks.

Metabolic networks comprise a multitude of enzymatic reactions carrying out various functions related to cell growth and product formation. Although such reactions are occasionally organized into biochemical pathways, a formal procedure is desired to identify the independent pathways in a bioreaction network and the degree of engagement of each individual reaction in these pathways. We present a procedure for the identification of the independent pathways of bioreaction networks of any size and complexity. The method makes use of the steady-state internal metabolite stoichiometry matrix and defines the independent pathways through the reaction membership of its kernel matrix. Examples from the aromatic amino acid biosynthetic pathway and central carbon metabolism of cells in culture are provided to illustrate the method. Applications to the analysis of the control structure of bioreaction networks are also discussed.     

Analysis of metabolic pathway using hybrid properties

Given a compounds-forming system, i.e., a system consisting of some compounds and their relationship, can it form a biologically meaningful pathway? It is a fundamental problem in systems biology. Nowadays, a lot of information on different organisms, at both genetic and metabolic levels, has been collected and stored in some specific databases. Based on these data, it is feasible to address such an essential problem. Metabolic pathway is one kind of compounds-forming systems and we analyzed them in yeast by extracting different (biological and graphic) features from each of the 13,736 compounds-forming systems, of which 136 are positive pathways, i.e., known metabolic pathway from KEGG; while 13,600 were negative. Each of these compounds-forming systems was represented by 144 features, of which 88 are graph features and 56 biological features. "Minimum Redundancy Maximum Relevance" and "Incremental Feature Selection" were utilized to analyze these features and 16 optimal features were selected as being able to predict a query compounds- forming system most successfully. It was found through Jackknife cross-validation that the overall success rate of identifying the positive pathways was 74.26%. It is anticipated that this novel approach and encouraging result may give meaningful illumination to investigate this important topic.     

An algorithm for linear metabolic pathway alignment

Metabolic pathway alignment represents one of the most powerful tools for comparative analysis of metabolism. It involves recognition of metabolites common to a set of functionally-related metabolic pathways, interpretation of biological evolution processes and determination of alternative metabolic pathways. Moreover, it is of assistance in function prediction and metabolism modeling. Although research on genomic sequence alignment is extensive, the problem of aligning metabolic pathways has received less attention. We are motivated to develop an algorithm of metabolic pathway alignment to reveal the similarities between metabolic pathways. A new definition of the metabolic pathway is introduced. The algorithm has been implemented into the PathAligner system; its web-based interface is available at http://bibiserv.techfak.uni-bielefeld.de/pathaligner/.     

Combinatorial complexity of pathway analysis in metabolic networks

Elementary flux mode analysis is a promising approach for a pathway-oriented perspective of metabolic networks. However, in larger networks it is hampered by the combinatorial explosion of possible routes. In this work we give some estimations on the combinatorial complexity including theoretical upper bounds for the number of elementary flux modes in a network of a given size. In a case study, we computed the elementary modes in the central metabolism of Escherichia coli while utilizing four different substrates. Interestingly, although the number of modes occurring in this complex network can exceed half a million, it is still far below the upper bound. Hence, to a certain extent, pathway analysis of central catabolism is feasible to assess network properties such as flexibility and functionality.     

Analysis of the aspartic acid metabolic pathway using mutant genes

Summary. Amino acid metabolism is a fundamental process for plant growth and development. Although a considerable amount of information is available, little is known about the genetic control of enzymatic steps or regulation of several pathways. Much of the information about biochemical pathways has arisen from the use of mutants lacking key enzymes. Although mutants were largely used already in the 60's, by bacterial and fungal geneticists, it took plant research a long time to catch up. The advance in this area was rapid in the 80's, which was followed in the 90's by the development of techniques of plant transformation. In this review we present an overview of the aspartic acid metabolic pathway, the key regulatory enzymes and the mutants and transgenic plants produced for lysine and threonine metabolism. We also discuss and propose a new study of high-lysine mutants. Received October 26, 2001 Accepted November 15, 2001     

Measuring multiple fluxes through plant metabolic networks

Fluxes through metabolic networks are crucial for cell function, and a knowledge of these fluxes is essential for understanding and manipulating metabolic phenotypes. Labeling provides the key to flux measurement, and in network flux analysis the measurement of multiple fluxes allows a flux map to be superimposed on the metabolic network. The principles and practice of two complementary methods, dynamic and steady-state labeling, are described, emphasizing best practice and illustrating their contribution to network flux analysis with examples taken from the plant and microbial literature. The principal analytical methods for the detection of stable isotopes are also described, as well as the procedures for obtaining flux maps from labeling data. A series of boxes summarizing the key concepts of network flux analysis is provided for convenience.     

Neural networks and linear programming for the satisfiability problem.

First a Linear Programming formulation is considered for the satisfiability problem, in particular for the satisfaction of a Conjunctive Normal Form in the Propositional Calculus and the Simplex algorithm for solving the optimization problem. The use of Recurrent Neural Networks is then described for choosing the best pivot positions and greatly improving the algorithm performance. The result of hard cases testing is reported and shows that the technique can be useful even if it requires a huge amount of size for the constraint array and Neural Network Data Input.     

Understanding alternative fluxes/effluxes through comparative metabolic pathway analysis of phylum actinobacteria using a simplified approach

Actinobacteria are known for their diverse metabolism and physiology. Some are dreadful human pathogens whereas some constitute the natural flora for human gut. Therefore, the understanding of metabolic pathways is a key feature for targeting the pathogenic bacteria without disturbing the symbiotic ones. A big challenge faced today is multiple drug resistance by Mycobacterium and other pathogens that utilize alternative fluxes/effluxes. With the availability of genome sequence, it is now feasible to conduct the comparative in silico analysis. Here we present a simplified approach to compare metabolic pathways so that the species specific enzyme may be traced and engineered for future therapeutics.     

Polymorphism at two loci through selection for linear metric deviation.

A model of phenotypic stabilising selection in which the fitness of an individual depends solely on its phenotype, and not directly on its genetic constitution, is explored algebraically for a system of two linked loci of unequal effect. It is found that selection for metric deviation gives rise to polymorphic gametefrequency equilibria for a variety of fitness regimes. Stability of non-trivial equilibria occurs for a wide range of parameter sets. Stability is facilitated by close linkage and inequality between gene effects. It is suggested that, in general genetic variation may be maintained under stabilising selection when the fitness of double heterozygotes exceeds that of the phenotypically intermediate homozygotes.     

Robust detection and verification of linear relationships to generate metabolic networks using estimates of technical errors

Background  

The size and magnitude of the metabolome, the ratio between individual metabolites and the response of metabolic networks is controlled by multiple cellular factors. A tight control over metabolite ratios will be reflected by a linear relationship of pairs of metabolite due to the flexibility of metabolic pathways. Hence, unbiased detection and validation of linear metabolic variance can be interpreted in terms of biological control. For robust analyses, criteria for rejecting or accepting linearities need to be developed despite technical measurement errors. The entirety of all pair wise linear metabolic relationships then yields insights into the network of cellular regulation.     

Functional integration of ecological networks through pathway proliferation

Large-scale structural patterns commonly occur in network models of complex systems including a skewed node degree distribution and small-world topology. These patterns suggest common organizational constraints and similar functional consequences. Here, we investigate a structural pattern termed pathway proliferation. Previous research enumerating pathways that link species determined that as pathway length increases, the number of pathways tends to increase without bound. We hypothesize that this pathway proliferation influences the flow of energy, matter, and information in ecosystems. In this paper, we clarify the pathway proliferation concept, introduce a measure of the node-node proliferation rate, describe factors influencing the rate, and characterize it in 17 large empirical food-webs. During this investigation, we uncovered a modular organization within these systems. Over half of the food-webs were composed of one or more subgroups that were strongly connected internally, but weakly connected to the rest of the system. Further, these modules had distinct proliferation rates. We conclude that pathway proliferation in ecological networks reveals subgroups of species that will be functionally integrated through cyclic indirect effects.     

Uncovering signal transduction networks from high-throughput data by integer linear programming

Signal transduction is an important process that transmits signals from the outside of a cell to the inside to mediate sophisticated biological responses. Effective computational models to unravel such a process by taking advantage of high-throughput genomic and proteomic data are needed to understand the essential mechanisms underlying the signaling pathways. In this article, we propose a novel method for uncovering signal transduction networks (STNs) by integrating protein interaction with gene expression data. Specifically, we formulate STN identification problem as an integer linear programming (ILP) model, which can be actually solved by a relaxed linear programming algorithm and is flexible for handling various prior information without any restriction on the network structures. The numerical results on yeast MAPK signaling pathways demonstrate that the proposed ILP model is able to uncover STNs or pathways in an efficient and accurate manner. In particular, the prediction results are found to be in high agreement with current biological knowledge and available information in literature. In addition, the proposed model is simple to be interpreted and easy to be implemented even for a large-scale system.     

Quantitative approaches for analysing fluxes through plant metabolic networks using NMR and stable isotope labelling

The quantitative analysis of metabolic networks is a prerequisite for understanding the integration and regulation of plant metabolism and for devising rational approaches for manipulating resource allocation in plants. The analysis of steady state stable isotope labelling experiments using nuclear magnetic resonance (NMR) spectroscopy has developed into a powerful method for determining these fluxes in micro-organisms and its application to heterotrophic plant metabolism is increasing. After an introductory discussion of the well known role of stable isotopes in pathway delineation, the review considers their application to metabolic flux analysis in plants. These applications are divided into two groups – small scale analyses of fluxes through particular pathways and large scale analyses of multiple fluxes through metabolic networks – and the problems caused by the complexity of intermediary metabolism in plants are discussed. It is concluded that metabolic flux analysis provides a powerful method for defining the metabolic phenotype of wild type, mutant and transgenic plants and that its development should be pursued.     

An integer linear programming approach for finding deregulated subgraphs in regulatory networks

Deregulation of cell signaling pathways plays a crucial role in the development of tumors. The identification of such pathways requires effective analysis tools that facilitate the interpretation of expression differences. Here, we present a novel and highly efficient method for identifying deregulated subnetworks in a regulatory network. Given a score for each node that measures the degree of deregulation of the corresponding gene or protein, the algorithm computes the heaviest connected subnetwork of a specified size reachable from a designated root node. This root node can be interpreted as a molecular key player responsible for the observed deregulation. To demonstrate the potential of our approach, we analyzed three gene expression data sets. In one scenario, we compared expression profiles of non-malignant primary mammary epithelial cells derived from BRCA1 mutation carriers and of epithelial cells without BRCA1 mutation. Our results suggest that oxidative stress plays an important role in epithelial cells of BRCA1 mutation carriers and that the activation of stress proteins may result in avoidance of apoptosis leading to an increased overall survival of cells with genetic alterations. In summary, our approach opens new avenues for the elucidation of pathogenic mechanisms and for the detection of molecular key players.     

Predicting selective drug targets in cancer through metabolic networks

The interest in studying metabolic alterations in cancer and their potential role as novel targets for therapy has been rejuvenated in recent years. Here, we report the development of the first genome‐scale network model of cancer metabolism, validated by correctly identifying genes essential for cellular proliferation in cancer cell lines. The model predicts 52 cytostatic drug targets, of which 40% are targeted by known, approved or experimental anticancer drugs, and the rest are new. It further predicts combinations of synthetic lethal drug targets, whose synergy is validated using available drug efficacy and gene expression measurements across the NCI‐60 cancer cell line collection. Finally, potential selective treatments for specific cancers that depend on cancer type‐specific downregulation of gene expression and somatic mutations are compiled.